Problem: Simplify the following expression: $q = \dfrac{36x + 48}{120x - 84}$ You can assume $x \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $36x + 48 = (2\cdot2\cdot3\cdot3 \cdot x) + (2\cdot2\cdot2\cdot2\cdot3)$ The denominator can be factored: $120x - 84 = (2\cdot2\cdot2\cdot3\cdot5 \cdot x) - (2\cdot2\cdot3\cdot7)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $q = \dfrac{(12)(3x + 4)}{(12)(10x - 7)}$ Dividing both the numerator and denominator by $12$ gives: $q = \dfrac{3x + 4}{10x - 7}$